Two likely 2012 Republican presidential candidates face the same potential barrier to winning their party's primary: President Obama has said nice things about them.

Obama joked a few weeks weeks ago about the possibility of his ambassador to China, Jon Huntsman, running for president, saying "I'm sure that him having worked so well with me will be a great asset in any Republican primary." And White House officials, including the president, spent much of last year praising the health-care law that passed in Massachusetts in 2006, likening it to the federal legislation Obama signed into law, in obvious reference to former Massachusetts governor Mitt Romney.

Romney "did some interesting things there on health care, you know," Obama adviser David Axelrod said in an interview with USA Today that was published Monday. "We got some good ideas from him."

Romney has been planning his campaign for more than two years, while Huntsman's resignation Monday from his ambassadorship is expected to be the first move in his presidential run. And one major question for both men will be whether their links to Obama are truly fatal in a Republican primary.

To say the president is unpopular among potential Republican primary voters would be an understatement: The 2010 Republican primaries for congressional seats often turned into Obama-bashing contests, with the winner being the person who most explicitly distanced himself from the president's agenda.

In theory, working in the president's administration, as Obama himself joked, would seem more toxic. But it's not as if Huntsman was involved in writing the health-care law or the stimulus plan; the U.S. policy on China is not likely to emerge as a major issue in the GOP primary and it's not one that cuts along partisan lines.

On the other hand, one of the chief planks of what conservatives now call Obamacare is the idea that everyone must purchase health insurance, a requirement that Republican state attorneys general are saying is unconstitutional. Many health-care experts argue such a mandate is not only constitutional, but necessary.

Romney praised the idea of a mandate in 2005 and 2006; his opponents in 2011 are likely to remind voters of that repeatedly and toss Obama's name in as well.

Romney seems aware of the potential problem his support for the mandate could pose. In an interview Tuesday morning with ABC News, when pressed Romney hedged on his support of it, saying "I'm indicating that we (Massachusetts) went in one direction, and there are other possible directions."

"I'm not apologizing for it," Romney said. "I'd like to see states pursue their own ideas, see which ideas work best. That was the whole idea of our federal democracy. "

Obama today

The president has no public events for the second straight day. White House officials said they have not canceled events because of the Egypt situation; they said the president did not have any previously planned. Obama will meet with his Cabinet, Secretary of Defense Robert Gates and the Technology CEO Council, a group of top officials at companies such as Dell.

Bloomberg vs. Obama on guns

New York Mayor Michael Bloomberg, among the nation's leading advocates for stricter gun laws, is continuing to push the Obama administration on the issue.

"At a City Hall news conference Monday, Bloomberg showed videos of what the New York sleuths turned up at an Arizona gun show.

In a performance straight out of Hollywood, an investigator is seen handling a semiautomatic pistol that he is thinking about buying from a dealer at a Jan. 23 Crossroads of the West gun show in Phoenix.

Sounding sinister, he says, 'I like the concealability, it's the best part,' and admits he couldn't pass the background check required to buy a gun from a licensed dealer - but not from a private dealer like the one at the gun show. He then hands over a wad of cash and walks away with the pistol.

'That sale was blatantly illegal,' said Bloomberg, explaining that private sellers are not supposed to forgo checks if they have a reason to believe buyers are felons, mentally ill or couldn't pass federal scrutiny. 'But it happens all the time.' "